Summary: Proving Lower Bounds via Pseudo-Random
Generators
Manindra Agrawal
Department of Computer Science
Indian Institute of Technology, Kanpur
manindra@iitk.ac.in
Abstract. In this paper, we formalize two stepwise approaches, based
on pseudo-random generators, for proving P = NP and its arithmetic
analog: Permanent requires superpolynomial sized arithmetic circuits.
1 Introduction
The central aim of complexity theory is to prove lower bounds on the complexity
of problems. While the relative classification of problems (via reductions) has
been very successful, not much progress has been made in determining their
absolute complexity. For example, we do not even know if NE admits nonuniform
NC1
circuits.
Initial attempts (in 1970s) to prove lower bounds centered on using the diag-
onalization technique that had proven very useful in recursion theory. However,
a series of relativization results soon showed that this technique cannot help in
its standard guise [6]. Very recently, the technique has been used to prove cer-